Private
McGonagall would rip you to shreds if you played a prank on her... She's a very, very stern woman but with a cheeky side if you know her well enough. I was thinking more on the level of Ministers and such, like you say. Each Minister is different - some of the men haven't been that great either. And the first female Minister made great strides in international cooperation.
And if I recall correctly, which I didn't but I have a book your current Minister is Evangeline Orpington. Once King's Cross Station is built in a couple of years in your time, she'll establish Platform Nine-And-Three-Quarters in the station as the place to board the Hogwarts Express in London. Very clever bit of magic that one.
Do it when you want, not when you need. Makes it more fun that way.